On an indefinite semilinear elliptic problem on \(\mathbb R^N\)
type: Item
instance of: scholarly article
title: On an indefinite semilinear elliptic problem on \(\mathbb R^N\)
zbMATH Open document ID: 1127.35016
author: Nasreddine Megrez
author: Jacques Giacomoni
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-10-01T00:00:00Z
review text: This paper is devoted to the study of non-negative weak solutions of the bifurcation elliptic problem \(-\Delta u=\lambda h(x)u+g(x)u^p\) in \({\mathbb R}^N\), where \(N>2\), \(\lambda\in {\mathbb R}\), \(1<p<(N+2)/(N-2)\), and \(h(x)\) and \(g(x)\) are sign changing potentials. The main result of the present paper establishes the existence of a continuum of positive solutions, bifurcating from the principal eigenvalues \(\lambda_{1,h}\) and \(-\lambda_{1,-h}\) of the associated linear problem. The proof is based on the global bifurcation theorem of \textit{P. Rabinowitz} [J. Funct. Anal. 7, 487--513 (1971; Zbl 0212.16504)], combined with standard \textit{a priori} estimates of positive solutions.
reviewed by: Vicenţiu D. Rădulescu
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 58J55
zbMATH DE Number: 2105437
zbMATH Keywords: indefinite semilinear elliptic problem
zbMATH Keywords: principal eigenvalue
zbMATH Keywords: bifurcation
zbMATH Keywords: Kelvin transform
zbMATH Keywords: method of moving planes
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.04.056
OpenAlex ID: W2060778157
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DOI: 10.1016/J.JMAA.2004.04.056
description: scientific article; zbMATH DE number 2105437